| Description |
1 online resource : illustrations. |
| Series |
Idiot's guides |
|
Idiot's guides.
|
| Note |
Includes index. |
| Summary |
"Let's face it: the thought of Calculus I can be daunting. But it needn't be. in this helpful guide, the fundamentals of Calculus I are taught in easy-to-understand terms, with lots of explanatory graphs and illustrations and over 150 practice problems that feature simple, step-by-step solutions to really explain what you need to know,"-- Provided by publisher. |
| Contents |
Intro -- Contents iii -- Part 1: The Roots of Calculus 1 -- 1 What Is Calculus, Anyway? 3 -- What's the Purpose of Calculus? 4 -- Finding the Slopes of Curves 4 -- Calculating the Area of Bizarre Shapes 4 -- Justifying Old Formulas 5 -- Calculating Complicated x-Intercepts 5 -- Visualizing Graphs 5 -- Finding the Average Value of a Function 6 -- Calculating Optimal Values 6 -- Who's Responsible for This? 7 -- Ancient Influences 7 -- Newton vs Leibniz 9 -- I Ever Learn This? 11 -- 2 Polish Up Your Algebra Skills 13 -- Walk the Line: Linear Equations 14 -- Common Forms of Linear Equations 14 -- Calculating Slope 16 -- Interpreting Linear Graphs 18 -- You've Got the Power: Exponential Rules 21 -- Breaking Up Is Hard to Do: Factoring Polynomials 22 -- Greatest Common Factor 23 -- Special Factoring Patterns 23 -- Solving Quadratic Equations 24 -- Method One: Factoring 25 -- Method Two: Completing the Square 25 -- Method Three: The Quadratic Formula 26 -- Synthesizing the Quadratic Solution Methods 27 -- 3 Equations, Relations, and Functions 31 -- What Makes a Function Tick? 31 -- Working with Graphs of Functions 36 -- Functional Symmetry 39 -- Graphs to Know by Heart 43 -- Constructing an Inverse Function 45 -- Parametric Equations 47 -- What's a Parameter? 47 -- Converting to Rectangular Form 48 -- 4 Trigonometry: Last Stop Before Calculus 51 -- Getting Repetitive: Periodic Functions 51 -- Introducing the Trigonometric Functions 53 -- Sine (Written as y = sin x) 54 -- Cosine (Written as y = cos x) 54 -- Tangent (Written as y = tan x) 55 -- Cotangent (Written as y = cot x) 56 -- Secant (Written as y = sec x) 57 -- Cosecant (Written as y = csc x) 57 -- What's Your Sine: The Unit Circle 59 -- Incredibly Important Identities 61 -- Pythagorean Identities 62 -- Double-Angle Formulas 63 -- Solving Trigonometric Equations 64. |
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Part 2: Laying the Foundation for Calculus 67 -- 5 Take It to the Limit 69 -- What Is a Limit? 70 -- Can Something Be Nothing? 71 -- One-Sided Limits 74 -- When Does a Limit Exist? 78 -- When Does a Limit Not Exist? 79 -- 6 Evaluating Limits Numerically 85 -- The Major Methods 86 -- Substitution Method 86 -- Factoring Method 87 -- Conjugate Method 88 -- What If Nothing Works? 90 -- Limits and Infinity 90 -- Vertical Asymptotes 90 -- Horizontal Asymptotes 92 -- Special Limit Theorems 96 -- Evaluating Limits Graphically 97 -- Technology Focus: Calculating Limits 99 -- 7 Continuity 103 -- What Does Continuity Look Like? 104 -- The Mathematical Definition of Continuity 104 -- Types of Discontinuity 109 -- Jump Discontinuity 109 -- Point Discontinuity 113 -- Infinite/Essential Discontinuity 114 -- Removable vs Nonremovable Discontinuity 117 -- The Intermediate Value Theorem 118 -- 8 The Difference Quotient 121 -- When a Secant Becomes a Tangent 122 -- Honey, I Shrunk the x 123 -- Applying the Difference Quotient 127 -- The Alternate Difference Quotient 129 -- Part 3: The Derivative 131 -- 9 Laying Down the Law for Derivatives 133 -- When Does a Derivative Exist? 134 -- Discontinuity 134 -- Sharp Point in the Graph 134 -- Vertical Tangent Line 135 -- Basic Derivative Techniques 136 -- The Power Rule 136 -- The Product Rule 138 -- The Quotient Rule 139 -- The Chain Rule 140 -- Rates of Change 141 -- Trigonometric Derivatives 144 -- Tabular and Graphical Derivatives 145 -- Technology Focus: Calculating Derivatives 150 -- 10 Common Differentiation Tasks 155 -- Finding Equations of Tangent Lines 156 -- Implicit Differentiation 159 -- Differentiating an Inverse Function 161 -- Parametric Derivatives 164 -- Technology Focus: Solving Gross Equations 166 -- Using the Built-In Equation Solver 166 -- The Equation-Function Connection 170. |
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11 Using Derivatives to Graph 173 -- Relative Extrema 174 -- Finding Critical Numbers 175 -- Classifying Extrema 176 -- The Wiggle Graph 178 -- The Extreme Value Theorem 180 -- Determining Concavity 182 -- Another Wiggle Graph 183 -- The Second Derivative Test 184 -- 12 Derivatives and Motion 187 -- The Position Equation 188 -- Velocity 190 -- Acceleration 191 -- Vertical Projectile Motion 193 -- 13 Common Derivative Applications 195 -- Newton's Method 196 -- Evaluating Limits: L'Hôpital's Rule 199 -- More Existence Theorems 200 -- The Mean Value Theorem 201 -- Rolle's Theorem 203 -- Related Rates 204 -- Optimization 208 -- Part 4: The Integral 215 -- 14 Approximating Area 217 -- Riemann Sums 218 -- Right and Left Sums 219 -- Midpoint Sums 221 -- The Trapezoidal Rule 222 -- Simpson's Rule 225 -- 15 Antiderivatives 227 -- The Power Rule for Integration 228 -- Integrating Trigonometric Functions 230 -- Separation 232 -- The Fundamental Theorem of Calculus 233 -- Part One: Areas and Integrals Are Related 233 -- Part Two: Derivatives and Integrals Are Opposites 235 -- u-Substitution 236 -- Tricky u-Substitution and Long Division 237 -- Technology Focus: Definite and Indefinite Integrals 239 -- 16 Applications of the Fundamental Theorem 245 -- Calculating Area Between Two Curves 246 -- The Mean Value Theorem for Integration 249 -- A Geometric Interpretation 249 -- The Average Value Theorem 251 -- Finding Distance Traveled 253 -- Accumulation Functions 255 -- Arc Length 256 -- Rectangular Equations 256 -- Parametric Equations 257 -- Part 5: Differential Equations and More 259 -- 17 Differential Equations 261 -- Separation of Variables 262 -- Types of Solutions 263 -- Family of Solutions 264 -- Specific Solutions 266 -- Exponential Growth and Decay 267 -- 18 Visualizing Differential Equations 275 -- Linear Approximation 276 -- Slope Fields 277. |
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Euler's Method 281 -- Technology Focus: Slope Fields 285 -- 19 Final Exam 289 -- A Solutions to "You've Got Problems" 301 -- B Glossary 317 -- Index 323. |
| Subject |
Calculus.
|
|
Calcul infinitésimal. |
|
calculus. |
|
Calculus |
| Added Title |
Calculus 1 |
|
Calculus one |
|
Idiot's guides Calculus I |
| Other Form: |
Original 1465451684 9781465451682 (OCoLC)925397912 |
| ISBN |
9781465454133 (electronic bk.) |
|
1465454136 (electronic bk.) |
|
9781465454126 |
|
1465454128 |
|
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